A third-round selection (72nd overall) by the Tampa Bay Lightning in the 2015 NHL Draft, Cirelli returned to the junior ranks and took over as captain of the OHL’s Oshawa Generals immediately after. He enjoyed a breakout campaign in 2016-17 as he was traded to the Erie Otters and won an OHL crown in addition to capturing a silver medal at the 2017 World Junior Championship. Jumping to the pro level with Tampa Bay’s AHL affiliate in Syracuse, he was promoted in the late stages of 2017-18 and put up 11 points in 18 NHL games after impressing with the Crunch.
Retaining the number 71 as he became a full-fledged member of the Lightning’s roster in 2018-19, he flirted with the 20-goal mark and finished sixth in voting for the Calder Trophy in addition to getting votes for the Selke Trophy thanks to his two-way skill. As a result, he was named to the NHL’s All-Rookie Team. He continued to show progress as a sophomore and surpassed the 40-point mark for the first time while ranking among the league leaders in plus-minus and shorthanded goals.